Data Source and Methodology
Calculations follow standard amortization math used in Truth in Lending (Regulation Z) Appendix J. Monthly interest is computed as APR ÷ 12, and extra payments are applied directly to principal each period after deducting interest. Lump sums reduce the balance immediately before the first period of the simulation.
Formulas Used
Monthly rate: \( r = \frac{\text{APR}}{12} \)
Baseline payment check: If \( P_{\text{mt}} \leq B \cdot r \) the payment is too small and the balance grows.
Iteration:
- Interest \( = B_{t-1} \cdot r \)
- Principal \( = \min\big(P_{\text{mt}} + E - \text{Interest},\, B_{t-1}\big) \)
- Balance \( = \max\big(B_{t-1} - \text{Principal},\, 0\big) \)
Total interest is the sum of interest across periods; the payoff month is reached when the balance becomes zero.
Worked Example
Balance $20,000, APR 6.5%, payment $450, extra $75/month, lump sum $1,000 today:
- Lump sum reduces balance to $19,000 before the first payment.
- Monthly interest initially ≈ $102.92; principal paid ≈ $422.08.
- With the extra $75, payoff occurs in ≈ 43 months instead of 51.
- Total interest drops from ≈ $3,148 to ≈ $2,589, saving ≈ $559.
Negative Amortization Warning
If your monthly payment is less than the monthly interest, the loan balance increases. The calculator flags this condition and asks for a higher payment or additional lump sum to guarantee payoff.